// Shunting Yard Algorithm+ −
// by Edsger Dijkstra+ −
// ========================+ −
+ −
object CW9a {+ −
+ −
type Toks = List[String]+ −
+ −
// the operations in the simple version+ −
val ops = List("+", "-", "*", "/")+ −
+ −
// the precedences of the operators+ −
val precs = Map("+" -> 1,+ −
"-" -> 1,+ −
"*" -> 2,+ −
"/" -> 2)+ −
+ −
// helper function for splitting strings into tokens+ −
def split(s: String) : Toks = s.split(" ").toList+ −
+ −
// (6) Implement below the shunting yard algorithm. The most+ −
// convenient way to this in Scala is to implement a recursive + −
// function and to heavily use pattern matching. The function syard + −
// takes some input tokens as first argument. The second and third + −
// arguments represent the stack and the output of the shunting yard + −
// algorithm.+ −
//+ −
// In the marking, you can assume the function is called only with + −
// an empty stack and an empty output list. You can also assume the+ −
// input os only properly formatted (infix) arithmetic expressions+ −
// (all parentheses will be well-nested, the input only contains + −
// operators and numbers).+ −
+ −
// You can implement any additional helper function you need. I found + −
// it helpful to implement two auxiliary functions for the pattern matching: + −
// + −
+ −
def is_op(op: String) : Boolean = ops.contains(op)+ −
+ −
def prec(op1: String, op2: String) : Boolean = precs(op1) <= precs(op2)+ −
+ −
+ −
def syard(toks: Toks, st: Toks = Nil, out: Toks = Nil) : Toks = (toks, st, out) match {+ −
case (Nil, _, _) => out.reverse ::: st+ −
case (num::in, st, out) if (num.forall(_.isDigit)) => + −
syard(in, st, num :: out)+ −
case (op1::in, op2::st, out) if (is_op(op1) && is_op(op2) && prec(op1, op2)) =>+ −
syard(op1::in, st, op2 :: out) + −
case (op1::in, st, out) if (is_op(op1)) => syard(in, op1::st, out)+ −
case ("("::in, st, out) => syard(in, "("::st, out)+ −
case (")"::in, op2::st, out) =>+ −
if (op2 == "(") syard(in, st, out) else syard(")"::in, st, op2 :: out)+ −
case (in, st, out) => {+ −
println(s"in: ${in} st: ${st} out: ${out.reverse}")+ −
Nil+ −
} + −
} + −
+ −
+ −
// test cases+ −
//syard(split("3 + 4 * ( 2 - 1 )")) // 3 4 2 1 - * ++ −
//syard(split("10 + 12 * 33")) // 10 12 33 * ++ −
//syard(split("( 5 + 7 ) * 2")) // 5 7 + 2 *+ −
//syard(split("5 + 7 / 2")) // 5 7 2 / ++ −
//syard(split("5 * 7 / 2")) // 5 7 * 2 /+ −
//syard(split("9 + 24 / ( 7 - 3 )")) // 9 24 7 3 - / ++ −
+ −
//syard(split("3 + 4 + 5")) // 3 4 + 5 ++ −
//syard(split("( ( 3 + 4 ) + 5 )")) // 3 4 + 5 ++ −
//syard(split("( 3 + ( 4 + 5 ) )")) // 3 4 5 + ++ −
//syard(split("( ( ( 3 ) ) + ( ( 4 + ( 5 ) ) ) )")) // 3 4 5 + ++ −
+ −
// (7) Implement a compute function that evaluates an input list+ −
// in postfix notation. This function takes a list of tokens+ −
// and a stack as argumenta. The function should produce the + −
// result as an integer using the stack. You can assume + −
// this function will be only called with proper postfix + −
// expressions. + −
+ −
def op_comp(s: String, n1: Int, n2: Int) = s match {+ −
case "+" => n2 + n1+ −
case "-" => n2 - n1+ −
case "*" => n2 * n1+ −
case "/" => n2 / n1+ −
} + −
+ −
def compute(toks: Toks, st: List[Int] = Nil) : Int = (toks, st) match {+ −
case (Nil, st) => st.head+ −
case (op::in, n1::n2::st) if (is_op(op)) => compute(in, op_comp(op, n1, n2)::st)+ −
case (num::in, st) => compute(in, num.toInt::st) + −
}+ −
+ −
// test cases+ −
// compute(syard(split("3 + 4 * ( 2 - 1 )"))) // 7+ −
// compute(syard(split("10 + 12 * 33"))) // 406+ −
// compute(syard(split("( 5 + 7 ) * 2"))) // 24+ −
// compute(syard(split("5 + 7 / 2"))) // 8+ −
// compute(syard(split("5 * 7 / 2"))) // 17+ −
// compute(syard(split("9 + 24 / ( 7 - 3 )"))) // 15+ −
+ −
}+ −
+ −
+ −